The rechargeable battery of Lego is very expensive. If you want a cheaper option, try this:
Insert 6 rechargeable NiMh batteries, batteries with low self-discharge are highly recommended (such as Ansmann max-e, Sanyo Eneloop, eneready).
Buy an AC adapter with 9V 300mA output (500mA is also ok) and a Bicycle lamp of 6V 2,4W. The lamp shall be placed in series to the AC adapter, like a fuse. Connect the AC adapter to the battery box of the NXT, in parallel to the batteries.
The lamp will regulate the charge current to approximately 250mA, which is less enough to leave out an intelligent charging controller and high enough to power the NXT computer (without motors).
It will charge empty batteries within about 10 hours when the NXT is switched off. And it can keep the battieries full if the NXT is running standby, not driving the motors, which allows applications to run continuously 24 hours each day.
The lamp will light softly and flicker a little sometimes.
When the batteries are full, the surplus energy will be transformed to heat by the batteries. But that's so less, we dont need to worry about.